VectorHard
Question
Let 
and 
be two non-colinear unit vectors. If 
and 
, then 
is
and be two non-colinear unit vectors. If and , then is Options
A.
B.
C.
D.
Solution
Let θ be the angle between 
and 
. Since, and are non-collinear vectors, then θ ≠ 0 and θ ≠ π
We have,
= 
= cosc θ
Now,
⇒
⇒
⇒
⇒
⇒
= 1 + cos2 θ - 2 cos2 θ
⇒ = 1 - cos2 θ
⇒ = sin2 θ
Also,
(given)
⇒
⇒
⇒
∴
Now,
∴
and . Since, and are non-collinear vectors, then θ ≠ 0 and θ ≠ π We have,
= = cosc θ
Now,
⇒
⇒
⇒
⇒
⇒
= 1 + cos2 θ - 2 cos2 θ ⇒
= 1 - cos2 θ ⇒
= sin2 θAlso,
(given) ⇒
⇒
⇒
∴
Now,
∴
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